so i'm really lost with inverses..

can someone just explain to me how to do it?

g(x)= 1-1/(x-1)

and

g^-1(x)= 1+1/(1-x)

how do you prove that they are or are not inverses?

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- Mar 25th 2009, 03:49 PMlonejunior[SOLVED] inverse functions
so i'm really lost with inverses..

can someone just explain to me how to do it?

g(x)= 1-1/(x-1)

and

g^-1(x)= 1+1/(1-x)

how do you prove that they are or are not inverses? - Mar 25th 2009, 03:59 PMHallsofIvy
I've lost track of how many times I've said this, but: by showing that the definition holds.

The definition of "inverse function" is:

$\displaystyle g^{-1}$ is the inverse function to g(x) if and only if $\displaystyle g^{-1}(g(x))= x$ and $\displaystyle g(g^{-1}(x))= x$.

If g(x)= 1- 1/(x-1) and $\displaystyle g^{-1}(x)= 1+ 1/(1- x)$, then [tex]g^{-1}(g(x))= g^{-1}(1- 1/(x-1))= 1+ 1/(1-[1-1/(x-1)]). Show that that is equal to x and the do it the other way.